Planning support from the values you enter — not professional advice.
Your SIN() takes radians
This is the angle mistake that actually costs people time, and it produces a plausible number rather than an error. Type =SIN(90) into a spreadsheet expecting 1, and you get 0.894.
Nothing is broken. The function took 90 radians, because every trigonometric function in every spreadsheet and every mainstream programming language expects radians — Excel, Google Sheets, JavaScript, Python, C, and the rest. 90 radians is a little over fourteen full turns, and its sine is 0.894.
The correct formula is =SIN(RADIANS(90)), which gives 1. Going the other way, an inverse function returns radians and needs =DEGREES(ASIN(1)) to come back to 90. The rule is simple once seen: wrap every angle going into a trig function in RADIANS(), and every angle coming out of one in DEGREES().
The reason radians are the default is not arbitrary. In radians the derivative of sine is cosine, and sin(x)/x tends to 1 as x tends to zero — both of which pick up awkward constant factors in degrees. The whole of calculus is cleaner in radians, so that is what the libraries implement, and the degree is left as a display convention.
Degrees, minutes and seconds
Angles are often written as a compound: 40° 26′ 46″ rather than 40.4461°. The subdivisions are sexagesimal, inherited from Babylonian arithmetic — one degree is 60 arcminutes, one arcminute is 60 arcseconds — which is the same structure as hours, minutes and seconds of time, and for the same historical reason.
The trap is identical to feet and inches: the decimal fraction is not the minutes. 40.5° is 40° 30′, not 40° 50′, because half a degree is thirty minutes. To convert a compound to decimal, divide the minutes by 60 and the seconds by 3,600 and add: 40 + 26/60 + 46/3600 = 40.4461°.
Coordinates are where most people meet this, and mixing the two notations is how a location ends up in the wrong place. 40° 26′ 46″ N is a point in Pennsylvania; 40.2646° N, the same digits read as a decimal, is roughly 22 kilometres south of it. Both are valid coordinates, which is exactly why the mistake is not caught by the mapping software.
One useful relationship for navigation: one arcminute of latitude is one nautical mile, by construction. So a coordinate difference of 5′ is five nautical miles north or south, without any conversion at all.
The only inexact factors on this site
Everywhere else in this category, the factors are exact by definition. An inch is exactly 25.4 mm; a pound is exactly 0.453 592 37 kg; a kibibyte is exactly 1,024 bytes. Those are agreements, not measurements, so the arithmetic carries no error at all.
Degrees and radians are different, because the relationship between them is π — an irrational number with no finite decimal or fractional representation. There is no exact rational factor to store, so this page carries π to 33 significant figures and truncates, and marks the conversion as approximate rather than defined.
In practice the distinction is academic: 33 figures is many orders of magnitude finer than any instrument. A surveyor works to arcseconds, a good theodolite to tenths of one, and radio astronomy to milliarcseconds — all of which sit comfortably within a dozen digits. But it is a genuine difference in kind, and a converter that presented a π-based factor with the same confidence as a defined one would be overstating what it knows.
Conversions among degrees, gradians, turns, arcminutes and arcseconds are exact, because all of them are defined against the full turn rather than against the radian. Only the crossing into radians is approximate.
Gradians, and where they survive
The gradian — also called the gon or the grade — divides a full turn into 400 rather than 360, so a right angle is exactly 100 gon. It was a product of the same metrication effort that produced the metre, on the reasoning that a decimal right angle is easier to work with than a 90-degree one.
It never displaced the degree in general use, but it did survive in European surveying, particularly in France, Germany and Scandinavia, where total stations and cadastral records still use it. A slope of 100 gon is vertical; 50 gon is 45 degrees.
It is worth recognising rather than using: a survey drawing quoting angles near 400, or a right angle written as 100, is in gradians, and reading those numbers as degrees produces an angle 11% off with nothing obviously wrong about it. Most scientific calculators have a DEG/RAD/GRAD mode switch, and a calculator left in GRAD is a common source of homework that is quietly wrong.
Doing it in a spreadsheet
=RADIANS(A1) and =DEGREES(A1) are the two functions worth memorising, and they should wrap every trig call in the sheet — going in and coming out respectively. Written by hand it is =A1*PI()/180 and =A1*180/PI(); using PI() rather than a typed 3.14159 keeps full precision.
For a compound angle, the conversion to decimal degrees is =D+M/60+S/3600 with the three parts in their own cells. Going back: =INT(A1) gives the degrees, =INT((A1-INT(A1))*60) the minutes, and =((A1-INT(A1))*60-INT((A1-INT(A1))*60))*60 the seconds — worth building once and keeping, because it is fiddly enough to get wrong each time.
A guard worth adding to any sheet that takes angle input: =IF(ABS(A1)>360,"check units",A1). An angle over 360 is usually a radian value that has landed in a degree column, and catching it at entry is cheaper than tracing it through a trig chain afterwards.
Related calculators
Where an angle usually goes next:
LengthMillimetres to miles on the exact 1959 factors, with the mil kept clearly apart from the millimetre — they differ 25-fold.
AreaSquare feet, square metres, acres and hectares, with the factors squared for you — a square metre is 10.76 sq ft, not 3.28.
Speedmph, km/h, m/s, ft/s and knots on exact factors, with the nautical mile behind the knot explained rather than assumed.
RoofingCalculate roof area, pitch, and roofing squares from a footprint, or estimate shingle bundles, metal sheets and weight, or flat-membrane materials and cost.
Slope PercentageConvert a slope between percentage grade, degrees, a 1:n ratio and rise per run, or find the fall to set out across a known distance.
Data StorageBytes, KB, MB, GB and TB alongside the binary KiB, MiB, GiB and TiB — and why a 1 TB drive shows as 931 GB.
Nothing here is fetched and there is no data feed. Unusually for this site, the factors are not all exact: π is irrational, so every degree-to-radian conversion is a truncation rather than a definition, and the tool says so. The sources settle the radian’s status in the SI and the convention — shared by spreadsheets and programming languages alike — that trigonometric functions take radians.
Math.sin() — the argument is in radiansMDN Web Docs, Mozilla · verified 2026-09-06 · That the same convention holds in programming languages, so the trap is not specific to spreadsheets
Almost every factor on this site is exact by definition. The ones on this page are not, and that is worth saying plainly: converting degrees to radians requires π, which is irrational, so the result is carried to 33 significant figures and truncated rather than being exactly representable. That is far beyond any practical need — a surveyor works to arcseconds, an astronomer to milliarcseconds, and both are many orders of magnitude coarser — but it is a real difference in kind from the rest of the category, and the tool marks it rather than presenting a π-based factor as though it were defined. Conversions between degrees, gradians, turns, arcminutes and arcseconds ARE exact among themselves, since they are all defined against the full turn. For survey control, celestial navigation or machine positioning, work from the instrument and the standard, which will specify both the unit and the precision expected.
Published the Angle Converter: degrees, radians, gradians, turns, arcminutes and arcseconds.
Built around the trap that produces a plausible wrong number rather than an error — every trigonometric function in every spreadsheet and mainstream language takes RADIANS, so SIN(90) returns 0.894 (the sine of 90 radians) rather than 1.
These are the ONLY inexact factors on the site, and the page says so: π is irrational, so degree-to-radian conversion is a truncation rather than a definition. Conversions among degrees, gradians, turns and the arc units are exact, being all defined against the full turn.
Covers degrees-minutes-seconds as a compound format, where reading 40° 26′ 46″ as 40.2646° puts a coordinate about 22 km out with nothing obviously wrong about it.
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